Unintegrated sea quark at small x and vector boson production

Parton-shower event generators that go beyond the collinear-ordering approximation at small x have so far included only gluon and valence quark channels at transverse momentum dependent level. In this contribution we provide a denition of a transverse momentum depend (TMD) sea quark distribution valid in the small x region, which is based on the TMD gluon-to-quark splitting function. As an example process we consider vector boson production in the forward direction of one of the protons. The qq ! Z matrix element (with one o-shell quark) is calculated in an explicit gauge invariant way, making use of high energy factorization.